Yes, but this is not a recommended practice. Because squash have male and female blooms and need bees for pollination, seed saved from this year's crop probably will not breed true when planted next year. This is especially true if you are growing more than one type of squash. If you are only growing one type of squash and there are no other types of squash in the area, then seed can be saved with a fairly high degree of genetic purity. If you are growing hybrid squash, do not save seeds as they will not breed true.
